Presents a complete proof of Connes' Index Theorem generalized to foliated spaces, alongside the necessary background from analysis, geometry, and topology. It thus provides a natural introduction to the basic ideas of noncommutative topology. This edition has improved exposition, an updated bibliography, an index, and covers new developments and applications.
This book presents a complete proof of Alain Connes Index Theorem generalized to foliated spaces. Connes result is itself an abstraction of the Atiyah-Singer index theorem to the context of foliated manifolds. The book brings together the necessary background from analysis, geometry, and topology. It thus provides a natural introduction to some of the basic ideas and techniques of noncommutative topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering new developments and applications since the first edition appeared.
